• Journal of Ocean Engineering and Technology
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• v.33 no.3
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• pp.229-235
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• 2019

In this study, a two-dimensional oscillating foil with forward speed in a propagating wave flow field was considered. The time-mean power to maintain the heaving and pitching motions of the foil was analyzed using the perturbation theory in an ideal fluid. The power, which was a non-linear quantity of the second-order, was expressed in terms of the quadratic transfer functions related to the mutual product of the heaving and pitching motions and incoming vertical flow. The effects of the pivot point and phase difference among the disturbances were studied. The negative power, which indicates energy extraction from the fluid, is shown as an example calculation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.1 s.104
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• pp.74-80
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• 2006

This paper presents the characteristics of electromagnetic field uniformity in a reverberation chamber that can be used alternatively for the analysis, test and evaluation of electromagnetic interference and immunity. The dual-band diffuser, which can be used at two different frequency bands in a reverberation chamber, is applied, and it is made of two different single-band Schroeder's Quadratic Residue Diffusers. The FDTD method is used to analyze the field characteristics. Compared with single-band diffuser, the dual-band diffuser shows the improvement in not only expansion of test frequency band but also in characteristics of the field uniformity, polarity, power efficiency, and tolerance. Therefore, the reverberation chamber with the dual-band diffuser is a better facility, for the analysis and measurement of electromagnetic interference and immunity, than the reverberation chamber with a single-band diffuser.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.796-803
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• 2003

The discrete ordinates interpolation method (DOIM) has shown good accuracy and versatile applicability for the radiation $problems^{(1,2)}$. The DOIM is a nonconservative method in that the intensity and temperature are computed only at grid points without considering control volumes. However, when the DOIM is used together with a finite volume algorithm such as $SIMPLER^{(3)}$, intensities at the control surfaces need to be calculated. For this reason, a 'quadratic' and a 'decoration' schemes are proposed and examined. They are applied to two kinds of radiation problem in one-dimensional geometries. In one problem, the intensity and temperature are calculated while the radiative heat source is given, and in the other, the intensity and the radiative heat source are computed with a given temperature field. The quadratic and the decoration schemes show very successful results. The quadratic scheme gives especially accurate results so that further decoration may not be needed. It is recommended that the quadratic and the decoration schemes may be used together, or, one of them may be applied for control volume radiative energy balance.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.2
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• pp.227-233
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• 2001

Electromagnetic field characteristics of Reverberation chamber, which could be applicable for an alternative test facility of electromagnetic interference and radiated electromagnetic susceptibility have been investigated. To obtain the required field uniformity of reverberation chamber, Schroeder method Quadratic Residue Diffuser was designed to be applied to chamber. In this paper, 3 different types of diffusers depending on diffuser's periodic direction have been used to investigate field characteristics of each type by using FDTD numerical method. The results show all 3 types of reverberation chambers have below $\pm$3 dB tolerance of field uniformity characteristics, and the symmetrical, type 3, structure show better results among them.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.18 no.6 s.121
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• pp.577-583
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• 2007

The field uniformity inside the reverberation chamber has been improved using sets of quadratic residue diffuser (QRD). The electromagnetic field inside the reverberation chamber with the dimension of $100{\times}80{\times}80cm$ has been analyzed by the finite-difference time-domain(FDTD) method. The calculated fields in a $40{\times}30{\times}30cm$ test volume have been sampled to obtain a standard deviation and field uniformity. Results show that the standard deviation of the calculated field and uniformity have been improved by varying angles and orientation of the inclined surfaces of the QRDs installed inside the reverberation chamber.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.123-132
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• 2021

Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars ResKLE decomposes (up to isogeny) into abelian varieties over K $$Res^L_KE{\sim}{\bigoplus_{F{\in}S}}A_F,$$ where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then AL is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, $L=K({\sqrt[3]{D}})$ is the cyclic cubic extension of K for some D ∈ K×/(K×)3, E = Ea : y2 = x3 + a is an elliptic curve with j-invariant 0 defined over K, and EaD : y2 = x3 + aD2 is the cubic twist of Ea. In this case, we prove AL is isogenous over K to $E_a^D{\times}E_a^{D^2}$ and a property of the Selmer rank of AL, which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.457-463
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• 2007

We show that any filter of Tarski algebra can be de-composed into the union of some sets. Moreover, we introduce the notion of expansions of filters in Tarski algebras, and discuss the notion of ${\sigma}$-primary filters in Tarski algebras. Finally, we show that there is no non-trivial quadratic Tarski algebras on a field X with $|X|{\geq}3$.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.131-146
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• 2018

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.